Kink oscillation (AIA 2010 Oct 16)
Multi-loop oscillations
Physical parameters of the loops
Estimation of the magnetic field
Conclusion and future work
Coronal seismology with two adjacent oscillating
loops
D. Yuan 1 , V.M. Nakariakov
1
1
and M.J. Aschwanden
2
CFSA, Department of Physics, University of Warwick
Gibbet Hill Road, CV4 7AL, Coventry, UK
2
Lockheed Martin Advanced Technology Center
Solar & Astrophysics Laboratory
Org. ADBS, Bldg. 252, 3251
Hanover St., Palo Alto, CA94304, USA
Email: Ding.Yuan@warwick.ac.uk
D. Yuan
Coronal seismology with two adjacent oscillating loops
Kink oscillation (AIA 2010 Oct 16)
Multi-loop oscillations
Physical parameters of the loops
Estimation of the magnetic field
Conclusion and future work
1
Kink oscillation (AIA 2010 Oct 16)
2
Multi-loop oscillations
3
Physical parameters of the loops
4
Estimation of the magnetic field
5
Conclusion and future work
D. Yuan
Coronal seismology with two adjacent oscillating loops
Kink oscillation (AIA 2010 Oct 16)
Multi-loop oscillations
Physical parameters of the loops
Estimation of the magnetic field
Conclusion and future work
M2.9 GOES-class flare and kink oscillating loops
AIA 195 A, 2010-10-16 19:22:36 UT
Oscillating Loop
NS (arcsec from Sun center)
-200
This event was already
presented by M.
Aschwanden. Our aim is
to present a further
analysis of this event.
Flare center
-400
-600
-800
0
200
400
600
EW (arcsec from Sun center)
800
Figure:
SDO/AIA 171 Å observation on flaring centre and oscillating loops in
2010 Oct 16 19:05 - 19:35 UT (Aschwanden & Schrijver ApJ 2011)
D. Yuan
Coronal seismology with two adjacent oscillating loops
Kink oscillation (AIA 2010 Oct 16)
Multi-loop oscillations
Physical parameters of the loops
Estimation of the magnetic field
Conclusion and future work
Transverse oscillations observed in multiple wavelengths
Observations in SDO/AIA 131Å,
171Å, 195Å, 221Å ,335Å, 94Å.
Most prominent in 131Å (top right
) and 171Å (bottom right).
131 Å
171 Å
D. Yuan
Coronal seismology with two adjacent oscillating loops
Kink oscillation (AIA 2010 Oct 16)
Multi-loop oscillations
Physical parameters of the loops
Estimation of the magnetic field
Conclusion and future work
Controversial results of Aschwanden & Schrijver Apj 2011
Coupled cross-sectional and density oscillation with identical
periods
No detectable amplitude damping over observed durations of
about four periods
D. Yuan
Coronal seismology with two adjacent oscillating loops
Kink oscillation (AIA 2010 Oct 16)
Multi-loop oscillations
Physical parameters of the loops
Estimation of the magnetic field
Conclusion and future work
Time distance image enhanced with nonlinear diffusion
filtering
At least two oscillating loops are
observed, likely to be a unresolved
loop bundle. Two adjacent loops
share roughly one footpoint, with
the other footpoints tens of pixels
apart.
Intensity variation is observed to
have same period, roughly 180° out
of phase with kink oscillation, it is
likely due to line-of-sight effect.
Figure:
a) Original time distance in 171 Å b) Filtered with
non-linear anisotropic diffusion, edge-preserved c) Filtered with
non-linear anisotropic diffusion, coherence-enhanced
D. Yuan
Coronal seismology with two adjacent oscillating loops
Kink oscillation (AIA 2010 Oct 16)
Multi-loop oscillations
Physical parameters of the loops
Estimation of the magnetic field
Conclusion and future work
Forward modelling of DEM
R
(T,x,y)
The flux is defined: Fλ (x, y) = dEMdT
Rλ (T ), Rλ (T ) is
the filter response function, dEM/dT is the emission
measure.
the DEM is simplified as
[log(T )−log(Tp (x,y))]2
dEM (T,x,y)
= EMp (x, y) exp(−
)
dT
2σ2 (x,y)
T
The best fitting is obtained by minimising the goodness-of-fit
P obs
model (x,y,λ )
k
χ2 (x, y) = (n−n1free ) k F (x,y,λσk2 )−F
(x,y,λ )
F
k
See Aschwanden & Boerner 2011 Solar Phys.
D. Yuan
Coronal seismology with two adjacent oscillating loops
Kink oscillation (AIA 2010 Oct 16)
Multi-loop oscillations
Physical parameters of the loops
Estimation of the magnetic field
Conclusion and future work
Forward modelling of DEM of the loops
A linear cross-sectional background is removed
2
0)
F obs (x) = Fλloop exp(− (x−x
) + B0 + B1 (x − x0 )
2
2σw
√
The loop width is defined w(s) = 2 2 ln 2σw (s) = 2.35σw (s)
The loop electron density
is estimate by assuming a unit filling
q
EM loop (s)
loop
factor, ne (s) =
w(s)
See Aschwanden & Boerner 2011 Solar Phys.
D. Yuan
Coronal seismology with two adjacent oscillating loops
Kink oscillation (AIA 2010 Oct 16)
Multi-loop oscillations
Physical parameters of the loops
Estimation of the magnetic field
Conclusion and future work
Temperature log(Te)
Measurement of loop #0
171 A
1680
1660
8.0
7.0
6.5
6.0
5.5
8.9
Density log(ne)
1640
1620
1600
log(Te)= 5.95+
5.95_ 0.10
0.05_ 0.09
log(σT)= 0.05+
7.5
0
5
10
15
20
25
30
20
25
30
20
25
30
25
30
log(ne)= 8.55+
8.55_ 0.08
8.8
8.7
8.6
8.5
8.4
Loop width w(Mm)
1580
3120
3140
3160
3180
3200
3220
3240
8.0
Figure:
Forward modelling measurement (Aschwanden &
Boerner 2011 Solar Phys.). First iteration: Te = [0.5, 10.] MK
with σ(Te ) = [0.1, 1.]. Second iteration:
Te1 = [Te0 ± 3∆Te0 ] MK σ(Te ) = [σ0 ± 3∆σ0 ]
12
10
0
5
10
15
w= 3.10_
3.10+ 0.34
8
6
4
2
0
5
Goodness-of-fit χ
1560
0
5
10
15
χ= 0.88_
0.88+ 0.46
4
3
2
1
0
0
D. Yuan
5
10
15
20
Loop length s[Mm]
Coronal seismology with two adjacent oscillating loops
Kink oscillation (AIA 2010 Oct 16)
Multi-loop oscillations
Physical parameters of the loops
Estimation of the magnetic field
Conclusion and future work
Temperature log(Te)
Measurement of loop #1
171 A
1680
1660
8.0
7.0
6.5
6.0
5.5
9.0
Density log(ne)
1640
1620
1600
log(Te)= 6.11+
6.11_ 0.03
0.06_ 0.05
log(σT)= 0.06+
7.5
0
5
10
15
20
15
20
15
20
10
15
Loop length s[Mm]
20
log(ne)= 8.67+
8.67_ 0.04
8.9
8.8
8.7
8.6
Loop width w(Mm)
1580
3100 3120 3140 3160 3180 3200 3220 3240
8.0
Figure:
Forward modelling measurement (Aschwanden &
Boerner 2011 Solar Phys.). First iteration: Te = [0.5, 10.] MK
with σ(Te ) = [0.1, 1.]. Second iteration:
Te1 = [Te0 ± 3∆Te0 ] MK σ(Te ) = [σ0 ± 3∆σ0 ]
12
10
0
5
10
w= 3.03_
3.03+ 0.30
8
6
4
2
0
5
Goodness-of-fit χ
1560
0
5
10
χ= 0.70_
0.70+ 0.39
4
3
2
1
0
0
D. Yuan
5
Coronal seismology with two adjacent oscillating loops
Kink oscillation (AIA 2010 Oct 16)
Multi-loop oscillations
Physical parameters of the loops
Estimation of the magnetic field
Conclusion and future work
Improvement and use of the forward-modelling data
The temperature Gaussian widths was limited by discretization
in previous studies, is thinner after a fine searching.
The measurement are performed in segments independently,
thus break the coherence of the loop properties. We can’t
accept the Te , ne , w profiles, based on the known physics of
coronal loops
A 3-point running averaging (edge-wrapped) is done to the
Te , ne , w.
D. Yuan
Coronal seismology with two adjacent oscillating loops
Kink oscillation (AIA 2010 Oct 16)
Multi-loop oscillations
Physical parameters of the loops
Estimation of the magnetic field
Conclusion and future work
Summary of the parameters
Original measurement:
Te = [0.5, 10.] MK
log(σT )) = [0.1, 1.0]
Improved measurement:
Te1 = [Te0 ± 3∆Te0 ] MK
log(σT ) = [σ0 ± 3∆σ0 ]
loop # 0
loop # 0
log(Te ) = 5.91 ± 0.12,
log(σT ) = 0.12 ± 0.04
log(Te ) = 5.95 ± 0.10,
log(σT ) = 0.05 ± 0.09
log(ne ) = 8.59 ± 0.14
log(ne ) = 8.55 ± 0.08
w = 3.11 ± 0.54
w = 3.10 ± 0.34
χ2 = 1.02 ± 0.48
χ2 = 0.88 ± 0.46
loop # 1
loop # 1
log(Te ) = 6.05 ± 0.1,
log(σT ) = 0.15 ± 0.08
log(Te ) = 6.11 ± 0.03,
log(σT ) = 0.06 ± 0.05
log(ne ) = 8.64 ± 0.08
log(ne ) = 8.67 ± 0.04
w = 2.7 ± 0.58
w = 3.03 ± 0.30
2
χ2 = 0.70 ± 0.39
χ = 0.96 ± 0.69
D. Yuan
Coronal seismology with two adjacent oscillating loops
Kink oscillation (AIA 2010 Oct 16)
Multi-loop oscillations
Physical parameters of the loops
Estimation of the magnetic field
Conclusion and future work
Corona Seismology : loop #0
We estimated the magnetic field with new electron density ne
q
L
B0 =
8πµmp ni (1 + ne /ni ) = 5.4 ± 1.0 G
P
p
σ 2 (L) + σ 2 (P ) + (0.5σ(ni ))2 + (0.5σ(ne /ni ))2 = 0.19
σ(B0 ) =
σ(L) = 0.14, σ(ni ) = 0.19
σ(P ) = 0.05, σ(ne /ni ) = 0.13
Bkink = 4.0 ± 0.7 G (Aschwanden & Schrijver 2011 ApJ)
BPFSS = 6 G
D. Yuan
Coronal seismology with two adjacent oscillating loops
Kink oscillation (AIA 2010 Oct 16)
Multi-loop oscillations
Physical parameters of the loops
Estimation of the magnetic field
Conclusion and future work
Corona Seismology of two loops
We obtain the ratio of the lengths in the image plane, ratio of
periods from forward modelling data, and the internal density ratio.
L0 P1 ne0 0.5
(
) = 0.69 ± 0.16
L P n
p1 0 e1
σ(B0 /B1 ) =
2σ 2 (L) + 2σ 2 (P ) + (0.5σ(ne0 ))2 + (0.5σ(ne1 ))2 = 0.2
B0
B1
=
σ(ne0 ) = 0.19 and σ(ne1 ) = 0.09
B1 = 7.8 ± 2.3 G
D. Yuan
Coronal seismology with two adjacent oscillating loops
Kink oscillation (AIA 2010 Oct 16)
Multi-loop oscillations
Physical parameters of the loops
Estimation of the magnetic field
Conclusion and future work
Conclusion
The Gaussian width of the loop temperature is thinner than previously
expected.
The seismological value of the magnetic field of loop # 0 is estimated to
be B0 = 5.4 ± 1.0 G, based on the refined density measurement, it
persistent with the potential field value 6 G.
The magnetic field of the fainter loop # 1 is estimated B1 = 7.8 ± 2.3
with relative parameters to the adjacent loop that is more visible and easy
to measure. This can be done with incomplete information and less
affords, it can be applied to non-prominent loops, and those observed in
other wavelengths.
Magnetic field gradient exist between two low-β coronal loops, total
plasma pressure is not balanced, indicating the existence of magnetic
twist?
if yes, The relative magnetic twist can be measured indirectly, in zero β
~ ∇)B
~
~ + B2 ) + (B·
=0
approximation: ∇(p
8π
4π
D. Yuan
Coronal seismology with two adjacent oscillating loops
Kink oscillation (AIA 2010 Oct 16)
Multi-loop oscillations
Physical parameters of the loops
Estimation of the magnetic field
Conclusion and future work
Future work
Improve the accuracy of the parameters.
Develop advanced, physics-based technique for the
determination of the density and temperature profiles.
Perform forward modelling to investigate the observed
intensity oscillation based on the cross-sectional density
profile.
Develop a technique to measure the magnetic field and
relative magnetic twist.
D. Yuan
Coronal seismology with two adjacent oscillating loops